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Max-flow min-cut theorem in quantum computing

Author

Listed:
  • Singh, Nongmeikapam Brajabidhu
  • Roy, Arnab
  • Saha, Anish Kumar

Abstract

The max-flow min-cut theorem in graph theory states that the maximum flow of a network is equal to the minimum cut of edges of the flow network. Max-flow and min-cut are related as two primal–dual linear programs. The theorem is applicable in applications like network connectivity, graph matching problems, transportation and logistics, and scheduling problems. The aim of the paper is to model the classical max-flow and min-cut theorem in quantum computing. Two well-known methods for quantum optimization are quantum annealing and quantum approximate optimization algorithm. The max-flow min-cut is converted to its equivalent model of the above two methods for execution in polynomial time. This paper shows detailed classical to quantum conversion, analysis, implementation, and result of the theorem.

Suggested Citation

  • Singh, Nongmeikapam Brajabidhu & Roy, Arnab & Saha, Anish Kumar, 2024. "Max-flow min-cut theorem in quantum computing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 649(C).
    • Handle: RePEc:eee:phsmap:v:649:y:2024:i:c:s0378437124004990
    DOI: 10.1016/j.physa.2024.129990
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    References listed on IDEAS

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    1. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
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